Chapter 17, Problem 44A

Interpretation Introduction

Interpretation: The concentration of dinitrogen tetroxide has to be calculated.

Concept introduction: For a balanced chemical reaction,

  $aA+bB\rightleftharpoons cC+dD$

The equilibrium expression is ratio of the concentration of the products to the concentration of the reactants. The concentration of each reactant/product is raised to a power corresponding to their coefficient in the balanced equation.

The law of chemical equilibrium is given by the equilibrium expression,

  $K=\frac{{\left[C\right]}^c{\left[D\right]}^d}{{\left[A\right]}^a{\left[B\right]}^b}$

The equilibrium constant is represented as $K.$

Answer to Problem 44A

The concentration of dinitrogen tetroxide is $\text{5}{\text{.4×10}}^{\text{-4}}\text{M}\text{.}$

Explanation of Solution

The given chemical reaction is,

  $N_2{O}_4\left(g\right)\rightleftharpoons 2N{O}_2\left(g\right)$

Given data,

The equilibrium concentration of $\left[N{O}_2\right]$ is $\text{0}\text{.0021}\text{M}\text{.}$

The equilibrium constant is $\text{8}{\text{.1×10}}^{\text{-3}}\text{.}$

For a balanced chemical reaction,

  $aA+bB\rightleftharpoons cC+dD$

Where,

• $A,B,C,D$ are chemical species.
• $a,b,c$ and $d$ are coefficients in the balanced equation.

The equilibrium expression is given as,

  $K=\frac{{\left[C\right]}^c{\left[D\right]}^d}{{\left[A\right]}^a{\left[B\right]}^b}$

Where,

  $K$ is the value of equilibrium constant.

For the given reaction, the expression for equilibrium constant is written as,

  $K=\frac{{\left[N{O}_2\right]}^2}{\left[N_2{O}_4\right]}$

Substitute the values of equilibrium concentration of nitrogen dioxide and equilibrium constant in the above expression,

  $\begin{array}{l}K=\frac{{\left[N{O}_2\right]}^2}{[N_2{O}_4]}\\ \left(\text{8}{\text{.1×10}}^{\text{-3}}\right)=\frac{{\left(\text{0}\text{.0021}\right)}^{\text{2}}}{[N_2{O}_4]}\\ N_2{O}_4=\text{5}{\text{.4×10}}^{\text{-4}}\text{M}\end{array}$

The concentration of dinitrogen tetroxide is $\text{5}{\text{.4×10}}^{\text{-4}}\text{M}\text{.}$

Conclusion

The concentration of dinitrogen tetroxide is $\text{5}{\text{.4×10}}^{\text{-4}}\text{M}\text{.}$